Basic Problems

We expect that basic problems can be solved even by generic computational bioelectromagnetic methods on weak computers. As such, compared to the other problems in the benchmark, we expect a very large number of computational methods/tools will be able to solve these problems with acceptable accuracy and computational costs.

1. Head-Sized Sphere

Problem 1 requires the solution of scattering from a homogeneous and a 4-layered head-sized sphere of 108-mm radius.

1a. Homogeneous Head-Sized Sphere

Solve the scattering problem and find these quantities of interest when the 108-mm radius sphere is filled homogeneously with the (frequency-dependent) IEEE head tissue-equivalent material [5] and is illuminated by these impressed sources.

	402 MHz		900 MHz		2.45 GHz
	$\epsr$	$\sigma$ (S/m)	$\epsr$	$\sigma$ (S/m)	$\epsr$	$\sigma$ (S/m)
IEEE head tissue equivalent	44.724	0.87	41.5	0.97	39.2	1.80

1b. 4-Layered Head-Sized Sphere

Solve the scattering problem and find these quantities of interest when the 108-mm radius sphere is piece-wise homogeneous and is illuminated by these impressed sources. The sphere is composed of four layers (from outer to inner) [1]: 4 mm skin (dry), 4 mm fat, 8 mm bone average (mean of bone cortical and bone marrow), and 92 mm brain average (mean of grey matter and white matter). The frequency-dependent material properties are obtained from [6]:

	402 MHz		900 MHz		2.45 GHz
	$\epsr$	$\sigma$ (S/m)	$\epsr$	$\sigma$ (S/m)	$\epsr$	$\sigma$ (S/m)
Skin Dry	46.741	0.68892	41.405	0.86674	38.007	1.464
Fat	5.5789	0.041151	5.462	0.051043	5.2801	0.10452
Bone Average	9.40725	0.0604105	8.97915	0.091759	8.33895	0.2446735
Brain Average	49.721	0.59178	45.8055	0.76653	42.539	1.51135